O-LevelAdditional MathematicsStraight line graphs4037/12 · May/June 2012 · Q119 Marks
The point P lies on the line joining A(−1, –5) and B(11, 13) such that AP = (1/3)AB.
- (i)Find the equation of the line perpendicular to AB and passing through P.[5]
- (ii)The line perpendicular to AB passing through P and the line parallel to the x-axis passing through B intersect at the point Q. Find the coordinates of the point Q.[2]
- (iii)Find the area of the triangle PBQ.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [B1, B1] B1 for each coordinate
- [B1] B1 for gradient of AB
- [B1] B1 for perpendicular gradient
- [B1] B1 on their perp gradient and their point P Must be y = ...
- [M1] M1 for use of y = 13 and their PQ equation.
- [A1] A1 for both coordinates (can be implied)
- [M1] M1 for a valid attempt at area = (1/2) × PQ × PB
- [A1] Matrix method using their coordinates correctly. (1/2) × QB × vertical perp height
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